arXiv subjects

Stefan Schaefer

Publications and source records attributed to Stefan Schaefer.

At least 19 recordsLinked to original sources

arXiv2025

Investigating a two-level algorithm for fermionic observables

We investigate the combination of a two-level sampling algorithm with distillation techniques to compute disconnected fermionic correlation functions. The method relies on a factorization of the quark propagator into domain-local contributions that depend only on the gauge fields within overlapping temporal regions, enabling independent submeasurements of each term through a two-level sampling strategy. The two-level estimators exhibit the expected $1/N_1^2$ scaling of the variance, up to exponential boundary effects, and achieve an exponential reduction of statistical errors at nearly the same computational cost as standard sampling. The method is tested on pure gauge ensembles, providing a controlled benchmark for its forthcoming application to dynamical QCD studies of glueball and isosinglet meson correlation functions.

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arXiv2025

Update on two-level sampling for glueball observables in quenched QCD

We report our progress in combining a two-level sampling algorithm with distillation techniques for calculations of disconnected diagrams in quenched QCD. The simulations are performed on a single ensemble at $\beta=6.0$ and volume $V=16^3\times 64$, and at a pion mass of $m_\pi\approx 760~\mathrm{MeV}$.

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arXiv2024

Exponential Error Reduction for Glueball Calculations Using a Two-Level Algorithm in Pure Gauge Theory

This study explores the application of a two-level algorithm to enhance the signal-to-noise ratio of glueball calculations in four-dimensional $\mathrm{SU(3)}$ pure gauge theory. Our findings demonstrate that the statistical errors exhibit an exponential reduction, enabling reliable extraction of effective masses at distances where current standard methods would demand exponentially more samples. However, at shorter distances, standard methods prove more efficient due to a saturation of the variance reduction using the multi-level method. We discuss the physical distance at which the multi-level sampling is expected to outperform the standard algorithm, supported by numerical evidence across different lattice spacings and glueball channels. Additionally, we construct a variational basis comprising 35 Wilson loops up to length 12 and 5 smearing sizes each, presenting results for the first state in the spectrum for the scalar, pseudoscalar, and tensor channels.

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arXiv2023

Performance of two-level sampling for the glueball spectrum in pure gauge theory

The computation of the glueball spectrum is particularly challenging due to the rapid decay of the signal-to-noise ratio of the correlation functions. To address this issue, advanced techniques such as gauge link smearing and the variational method are commonly employed to identify the spectrum before the signal diminishes significantly. However, a significant improvement in the signal-to-noise ratio can be achieved by utilising multilevel sampling techniques. In this talk, we present a study of the glueball spectrum in pure gauge theory with a two-level algorithm. Specifically, we explore the relation between noise reduction and the various multilevel parameters, such as the width of the dynamical regions and the number of submeasurements.

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arXiv2022

Learning Trivializing Gradient Flows for Lattice Gauge Theories

We propose a unifying approach that starts from the perturbative construction of trivializing maps by L\"uscher and then improves on it by learning. The resulting continuous normalizing flow model can be implemented using common tools of lattice field theory and requires several orders of magnitude fewer parameters than any existing machine learning approach. Specifically, our model can achieve competitive performance with as few as 14 parameters while existing deep-learning models have around 1 million parameters for $SU(3)$ Yang--Mills theory on a $16^2$ lattice. This has obvious consequences for training speed and interpretability. It also provides a plausible path for scaling machine-learning approaches toward realistic theories.

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arXiv2022

The influence of gauge field smearing on discretisation effects

When designing lattice actions, gauge field smearing is frequently used to define the lattice Dirac operator. Since the smearing procedure removes effects of ultraviolet fluctuations, the fermions effectively see a larger lattice spacing than the gauge fields. Creutz ratios, formed from ratios of rectangular Wilson loops, based on smeared gauge fields are adequate observables to investigate the effect of smearing since they do not need renormalisation and provide a measure of the physical forces felt by the fermions. We study their behaviour at various smearing radii (fixed in lattice units) and in particular how the smearing influences the scaling towards the continuum limit. Since we employ the Wilson gradient flow as smearing, the same Creutz ratios have another, well defined continuum limit, when the flow time is fixed in physical units. That continuum limit is reached with smaller corrections at finite $a$.

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arXiv2021

Scale Setting for CLS 2+1 Simulations

We present an update of the scale setting for $N_f=2+1$ flavor QCD using gradient flow scales and pseudo-scalar decay constants. We analyze the latest ensembles with $2+1$ flavors of non-perturbatively improved Wilson fermions generated by CLS for improved precision. Special care is taken to correct for mistuning by measuring directly the mass derivatives of the various observables. We determine $t_0$ with input taken from a combination of leptonic decay rates of the Pion and the Kaon.

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arXiv2020

Remarks on strange-quark simulations with Wilson fermions

In the simulation of QCD with 2+1 flavors of Wilson fermions, the positivity of the fermion determinant is generally assumed. We present evidence that this assumption is in general not justified and discuss the consequences of this finding.

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arXiv2020

Frequency-splitting estimators for single-propagator traces

In these proceedings we address the computation of quark-line disconnected diagrams in lattice QCD. The evaluation of these diagrams is required for many phenomenologically interesting observables, but suffers from large statistical errors due to the vacuum and random-noise contributions to their variances. Motivated by a theoretical analysis of the variances, we introduce a new family of stochastic estimators of single-propagator traces built upon a frequency splitting combined with a hopping expansion of the quark propagator, and test their efficiency in two-flavour QCD with pions as light as 190 MeV. The use of these estimators reduces the cost of the computation by one to two orders of magnitude over standard estimators depending on the fermion bilinear. As a concrete application, we show the impact of these findings on the computation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

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arXiv2019

Frequency-splitting estimators of single-propagator traces

Single-propagator traces are the most elementary fermion Wick contractions which occur in numerical lattice QCD, and are usually computed by introducing random-noise estimators to profit from volume averaging. The additional contribution to the variance induced by the random noise is typically orders of magnitude larger than the one due to the gauge field. We propose a new family of stochastic estimators of single-propagator traces built upon a frequency splitting combined with a hopping expansion of the quark propagator, and test their efficiency in two-flavour QCD with pions as light as 190 MeV. Depending on the fermion bilinear considered, the cost of computing these diagrams is reduced by one to two orders of magnitude or more with respect to standard random-noise estimators. As two concrete examples of physics applications, we compute the disconnected contributions to correlation functions of two vector currents in the isosinglet omega channel and to the hadronic vacuum polarization relevant for the muon anomalous magnetic moment. In both cases, estimators with variances dominated by the gauge noise are computed with a modest numerical effort. Theory suggests large gains for disconnected three and higher point correlation functions as well. The frequency-splitting estimators and their split-even components are directly applicable to the newly proposed multi-level integration in the presence of fermions.

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arXiv2018

Multi-level integration for meson propagators

The computation of many correlation functions in lattice QCD is severely hindered by a signal-to-noise problem. Recent developments in the factorization of both the fermion propagator and determinant pave the way for the implementation of multi-level Monte Carlo integration techniques for lattice QCD. In these proceedings we introduce new strategies for the estimation of the factorized contribution to the connected and disconnected diagrams for meson two-point functions. An estimator for the factorized connected diagram is constructed sequentially for a two-level integration scheme. For the disconnected diagram, we introduce an improved estimator by performing a frequency-splitting of traces, applicable with or without multi-level integration. Preliminary results in the quenched theory with a two-level integration scheme are presented.

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arXiv2018

New extended interpolating fields built from three-dimensional fermions

New extended interpolating operators made of quenched three dimensional fermions are introduced in the context of lattice QCD. The mass of the 3D fermions can be tuned in a controlled way to find a better overlap of the extended operators with the states of interest. The extended operators have good renormalization properties and are easy to control when taking the continuum limit. Moreover the short distance behaviour of the two point functions built from these operators is greatly improved. A numerical comparison with point sources and Jacobi smeared sources on dynamical 2+1 flavour configurations is presented.

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arXiv2018

Testing the event-chain algorithm in asymptotically free models

We apply the event-chain algorithm proposed by Bernard, Krauth and Wilson in 2009 to toy models of lattice QCD. We give a formal prove of stability of the algorithm. We study its performance at the example of the massive Gaussian model on the square and the simple cubic lattice, the $O(3)$-invariant non-linear $σ$-model and the $SU(3) \times SU(3)$ principle chiral model on the square lattice. In all these cases we find that critical slowing down is essentially eliminated.

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arXiv2017

Multi-boson block factorization of fermions

The numerical computations of many quantities of theoretical and phenomenological interest are plagued by statistical errors which increase exponentially with the distance of the sources in the relevant correlators. Notable examples are baryon masses and matrix elements, the hadronic vacuum polarization and the light-by-light scattering contributions to the muon g-2, and the form factors of semileptonic B decays. Reliable and precise determinations of these quantities are very difficult if not impractical with state-of-the-art standard Monte Carlo integration schemes. I will review a recent proposal for factorizing the fermion determinant in lattice QCD that leads to a local action in the gauge field and in the auxiliary boson fields. Once combined with the corresponding factorization of the quark propagator, it paves the way for multi-level Monte Carlo integration in the presence of fermions opening new perspectives in lattice QCD. Exploratory results on the impact on the above mentioned observables will be presented.

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arXiv2017

CLS 2+1 flavor simulations at physical light- and strange-quark masses

We report recent efforts by CLS to generate an ensemble with physical light- and strange-quark masses in a lattice volume of 192x96^3 at $β=3.55$ corresponding to a lattice spacing of 0.064 fm. This ensemble is being generated as part of the CLS 2+1 flavor effort with improved Wilson fermions. Our simulations currently cover 5 lattice spacings ranging from 0.039 fm to 0.086 fm at various pion masses along chiral trajectories with either the sum of the quark masses kept fixed, or with the strange-quark mass at the physical value. The current status of simulations is briefly reviewed, including a short discussion of measured autocorrelation times and of the main features of the simulations. We then proceed to discuss the thermalization strategy employed for the generation of the physical quark-mass ensemble and present first results for some simple observables. Challenges encountered in the simulation are highlighted.

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arXiv2017

Local multiboson factorization of the quark determinant

We discuss the recently proposed multiboson domain-decomposed factorization of the gauge-field dependence of the fermion determinant in lattice QCD. In particular, we focus on the case of a lattice divided in an arbitrary number of thick time slices. As a consequence, multiple space-time regions can be updated independently. This allows to address the exponential degradation of the signal-to-noise ration of correlation functions with multilevel Monte Carlo sampling. We show numerical evidence of the effectiveness of a two-level integration for pseudoscalar propagators with momentum and for vector propagators, in a two active regions setup. These results are relevant to lattice computation of the hadronic contributions to the anomalous magnetic moment of the muon and to heavy meson decay form factors.

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arXiv2017

Setting the scale for the CLS $2 + 1$ flavor ensembles

We present measurements of a combination of the decay constants of the light pseudoscalar mesons and the gradient flow scale $t_0$, which allow to set the scale of the lattices generated by CLS with $2 + 1$ flavors of non-perturbatively improved Wilson fermions. Mistunings of the quark masses are corrected for by measuring the derivatives of observables with respect to the bare quark masses.

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arXiv2017

Domain decomposition and multilevel integration for fermions

The numerical computation of many hadronic correlation functions is exceedingly difficult due to the exponentially decreasing signal-to-noise ratio with the distance between source and sink. Multilevel integration methods, using independent updates of separate regions in space-time, are known to be able to solve such problems but have so far been available only for pure gauge theory. We present first steps into the direction of making such integration schemes amenable to theories with fermions, by factorizing a given observable via an approximated domain decomposition of the quark propagator. This allows for multilevel integration of the (large) factorized contribution to the observable, while its (small) correction can be computed in the standard way.

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